The term microelectromechanical systems (“MEMS”) refers to devices having very small components (typically in the range of 1 μm to 1 cm) which often operate as sensors. Electronics may be integrated into the devices to convert physical effects (such as displacement of a proof mass) into electrical output signals. High performance MEMS sensor systems are typically based on closed-loop architectures to provide good linearity and large dynamic range. As one example of such architectures, many systems reported in the literature use sigma-delta modulated single-bit feedback with a MEMS proof mass as an integrated part of the loop filter.
H. Paulson, “MEMS-Based Capacitive Sensor”, U.S. Pat. No. 8,104,346, Jan. 31, 2012, employs this architecture in a capacitive-coupled MEMS accelerometer and provides a lucid explanation of the underlying principles. Naturally, the single-bit feedback system creates a substantial amount of quantization noise which others have attempted to address through various means. For example, the mechanical part of a voltage driven micro-machined inertial sensor can be described as a harmonic oscillator described by a second-order characteristic function. To reduce the in-band quantization noise, the loop filter can add electrically determined poles to the system transfer function. This approach has been demonstrated by Y. Dong, M. Kraft, C. Goilasch and W. Redman-White, “A high-performance accelerometer with a fifth-order sigma-delta modulator”, J. Micromechanics & Microengineering, 15 (2005) pp 22-29. They created a fifth order system by introducing three electrical poles.
A similar architecture is employed in a state-of-the-art device by H. Kulah, J. Chae, N. Yazdi, K. Najafi, “Noise analysis and characterization of a sigma-delta capacitive microaccelerometer”, IEEE J. Solid-State Circuits, 41 (2006), pp 352-361. They conclude that mass-residual motion is the dominant noise source at low sampling frequencies for systems operated in closed-loop mode, and suggest that the best way to overcome this limitation is by increasing the sampling frequency.
Another state-of-the-art example can be found in P. Zwahlen, A. Nguyen, Y. Dong, F. Rudolf, M. Pastre, H. Schmid, “Navigation-grade MEMS accelerometer”, published by Colibry, www.colibrys.com. They present both simulated and measured data, showing what they claim is excellent matching between simulation and measurement. However, careful inspection of their results indicates that in the frequency range from 500 Hz to 1 kHz they have “smearing” of high frequency quantization noise down into the upper part of the passband. We attribute this discrepancy to mass-residual motion.
Thus the conventional techniques for providing a high-performance MEMS accelerometer include the use of a single-bit sigma-delta feedback architecture with a high-order loop filter and/or a substantially elevated clock rate. These techniques add an undesirable performance requirements and complexity for the integrated electronics and, for the reasons explained further herein, can provide only a limited amount of performance improvement.
It should be understood that the specific embodiments given in the drawings and detailed description below do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill in the art to discern the alternative forms, equivalents, and other modifications that are encompassed in the scope of the claims.